The present invention relates to a disposable plastic closure or lid, designed for use in connection with paper and/or plastic containers of various types such as beverage cups, food tubs and the like as commonly used in the fast food industry. Many such closures have been provided by the prior art with a wide variety of techniques for effecting engagement of the lid with the container. Notwithstanding the provisions of the prior art, a need remains for a method and apparatus for securing container lids to the container whereby the lid will remain attached to the container when deformed and in the event the container is inadvertently tipped over or otherwise tumbles onto a solid surface. Such a secured lid is particularly needed in the fast food industry for serving liquid beverages.